Without the force of state or a private army it’s pretty difficult for anyone to leave anything to someone after they kick the bucket.

If you aren’t suggesting the state take away my ability to provide inheritance to my descendants, then what is the function of calling inheritance anti-democratic? Are you suggesting that a true democracy does not allow individuals to leave inheritance to their descendants?

As I understand it, legacy can be (and definitely is) used as a tool for wielding power, which (democracy wise) gets naturally viewed as a problem.

That's not to say that inheritance is bad or that it causes more harm than good. Personally, I think that denying inheritance will take away an important working drive for many people, which in turn will invite in the said people a cool off after achieving certain level of personal comfort. All that while the society at large would benefit more from the same people to fulfill their working potential than from diminishing whatever vector of risk to the optimal function of democracy. Also, whatever much or little one may achieve in life, at one point it must be passed to someone else, due to our mortal nature. I'd rather let the owners have control over how and whom they pass that to (i.e. to someone they know and maybe even had the chance to personally educate), as that to me seems the best setting for having things built in the long run.